Absorption mufflers have been known to have annular gaps and/or chambers, in which the sound-absorbing material, especially glass wool, is arranged. The sound-absorbing material is arranged around the blank of an inner shell or around an inner tube before the final mounting of the outer shell and before the outer shell is permanently connected to the inner shell or to the inner tube, e.g., via a fold or by welding. The arrangement of the noncompact, flexible sound-absorbing material in the areas intended for this purpose or in the chambers of an exhaust muffler intended for this purpose and the subsequent assembly of the exhaust muffler body are comparatively laborious and expensive operations.